Stability of Relative Equilibria for Coupled Rotational and Translational Motion

Details Stability of Relative Equilibria for Coupled Rotational and Translational Motion Stability of Relative Equilibria for Coupled Rotational and Translational Motion

May 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009dda....40.1001s&link_type=abstract

American Astronomical Society, DDA meeting #40, #10.01; Bulletin of the American Astronomical Society, Vol. 41, p.903

Astronomy and Astrophysics

Astronomy

Scientific paper

The stability of relative equilibria for two non-spherical mass distributions is studied. We account for the full rotational/translational interaction between the two bodies by using a mutual gravitational potential expanded to 2nd order in both bodies. This allows us to restrict the system to planar motion, thus simplifying our analysis. We find that, for a given value of angular momentum, there are several possible relative equilibria for the system -- however only one is energetically stable and corresponds to the minimum energy configuration of the system at a given value of angular momentum. Applying these analytical results to the fission of a contact binary asteroid, we find that all equal density bodies that are spun to fission will enter directly into an unstable relative equilibrium, with the conjugate stable relative equilibrium lying at a greater distance. Thus, any contact binary asteroid spun to fission will immediately enter a strongly evolving phase of dynamical evolution. These results extend to the stability of nearly spherical bodies in contact, spun to fission, leading to the surprising result that a circular Keplerian orbit may actually be unstable when rotational coupling is allowed.

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